دانلود رایگان مقاله تنظیم صفحه مش برای مسائل بهینه سازی شکل مبتنی بر گره

Abstract

An iterative procedure to solve the inverse problem of detecting multiple voids in piezoelectric structure is proposed. In each iteration the forward problem is solved for various void configurations, and at each iteration, the mechanical and electrical responses of a piezoelectric structure is minimized at known specific points along the boundary to match the measured data. The Extended Finite Element method (XFEM) is employed for determining the responses as it allows the use of a fixed mesh for varying void geometries. The numerical method based on combination of classical shape derivative and of the level-set method for front propagation used in structural optimization is utilized to minimize the cost function. The results obtained show that this method is effectively able to determine the number of voids in a piezoelectric structure and its corresponding locations and shapes.

6. Conclusion

In this paper a methodology to detect multiple crack and void locations in a piezoelectric specimen is proposed. In each iteration, XFEM is used to solve the direct problem. The mesh remains unchanged in all iterations thereby considerably reducing computational time. The shape derivative and level sets are used to minimize the objective function. An adjoint problem is solved in each iteration to determine the shape derivative. Multiple setups are used to overcome the problem of local optima. The void configuration does not require external parameterization as it is implicitly represented by level sets. The numerical examples demonstrate the efficiency of the method in detecting any number of cracks and voids in specimen. The method proposed is more robust compared to iterative methods previously proposed in literature in which Genetic or search algorithms are used for the optimization. The method requires uniformly distributed voids all over the domain as initial configuration and so the method is not completely independent of initialization. In the future, the methodology will be extended to 3D and the response of piezoelectric specimen under dynamic loads may be utilized to construct the objective function.